Thermal roughening of the copper (110) surface: An x-ray diffraction experiment

Abstract

The roughness of the (110) surface of face-centered-cubic copper has been measured between 200 and 700 °C, by x-ray diffraction. The changes observed are reversible and suggest a roughening temperature of TR-600°C. This value is compared with simple theoretical estimates and found to be in satisfactory agreement.PACS numbers: 61.50. Cj, 64.60.Cn, 68.35.Bs A fundamental understanding of crystal surfaces and interfaces is a goal with many applications in physics, chemistry, and metallurgy, ranging from surface reconstructions to wetting and adhesion, catalysis, crystal growth, and sintering. Perhaps the simplest interface one can conceive is an atomically smooth, low-index facet that separates a crystallizing element from its vapor. However, a recurrent theoretical idea of the last thirty years is that of a surface-roughening transition, 1 which may occur at a much lower temperature than bulk melting. Below the roughening-transition temperature (TR), the interface corresponds more or less to the ideal, but for T>TR, its behavior is determined by surface stiffness. Therefore, capillary waves cause the interfacial position to fluctuate. Microscopically, this is achieved through the proliferation of atomic steps. The transition has attracted attention recently in the context of the equilibrium crystal shapes (ECS), 2 especially of 4 He crystals. 3 The connection is that, for a particular facet to occur on the ECS, the temperature must be below TR for that face. However, there have been few experimental studies of the microscopic aspects of interfacial roughening.Here, I report the results of an x-ray-diffraction study of the (110) face of face-centered-cubic (fee) copper, for temperatures between 200 and 700 °C. It is shown that the root mean square roughness ((w 2 ) l/2 ) of this surface changes reversibly with temperature, by measurements of the Bragg reflectivity far from Bragg peaks. From the temperature dependence of (w 2 ) 1/2 , T R -600°C is deduced. Finally, the values of both (u 2 ) l/2 and TR are compared favorably to simple theoretical estimates. These experiments provide the first direct observation of a roughening transition of a low-index face of a metal crystal. The choice of copper was motivated in part by extensive studies of the ECS of small (5-jum) metal crystals. 4,5 Specifically, it is known that the (110) face of copper is absent from the ECS immediately below its melting temperature (T m =1083 o C). 5 In addition, the He-diffraction measurements of Lapujoulade and coworkers 6 on faces of copper vicinal to the (100) suggest that the (113), (115), and (117) faces undergo roughening transitions. A comparison between the behavior of the (110) face and these stepped surfaces may lead to a better general understanding of the orientation dependence of metal surface stiffness. Finally, it is worth mentioning that while the techniques of microscopy and atom diffraction probe significantly different length scales-microns in the former case and several tens of angstroms in the latter-one advantage of x-ray...

Temperature dependent structure of low index copper surfaces studied by molecular dynamics simulation

“…These experimental techniques have been applied to study the copper (010), (110) and (111) surfaces. The results for the (110) face have shown an enhancement of the disorder for temperatures above T = 550K and a roughening transition at T R = 870K [9] and T R = 1070K [10]. For the (010) face, LEED experiments show an enhancement of the atoms vibrational amplitude at the surface [11].…”

“…These behaviours have been attributed to strong anharmonic vibrations of the atoms at the surface. This anharmonicity brings disorder to the surface, mainly at high temperatures [8,9,10]. These experimental techniques have been applied to study the copper (010), (110) and (111) surfaces.…”

Disordering Transitions of Metal Surfaces

“…During the commensurate-incommensurate transition, the surface both roughens and deconstructs. Preliminary reports of these results have been published elsewhere [1,5].…”

Thermal dynamics at surfaces

“…X-ray scattering data obtained on Cu(110) have initially been interpreted in terms of surface roughening [77]. Since all other scattering experiments on this surface were reminiscent of surface anharmonicity, it is very likely that also the X-ray data can be reconciled this way.…”